Question:
The first non-zero Fourier coefficient in the expansion of \( \sin^3(x) \) is:
The first non-zero Fourier coefficient in the expansion of \( \sin^3(x) \) is:
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Fourier series represents functions as sums of sine and cosine terms.
Updated On: Mar 26, 2025
- \( 0.25 \)
- \( 0.75 \)
- \( 1 \)
- \( -0.5 \)
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The Correct Option is D
Solution and Explanation
Using Fourier expansion,
\[ \sin^3(x) = \frac{3}{4} \sin x - \frac{1}{4} \sin(3x) \] The first non-zero coefficient is \( -0.5 \).
\[ \sin^3(x) = \frac{3}{4} \sin x - \frac{1}{4} \sin(3x) \] The first non-zero coefficient is \( -0.5 \).
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